After doing a bit of research, I settled on the aeroquad flight software.
The brains of the device are an android adk board
with the aeroquad mega shield. (I chose the android adk because I'm planning on trying to use an android phone as a platform for
computer vision and telemetry.) Currently
the only sensors on the board are a 3-axis gyroscope and a 3-axis accelerometer (with empty pinouts for a barometer
and magnetometer).

The airframe is made of a frame of birch ply 24 inches in diameter, with the arduino mounted on an aluminum plate with standoffs and covered with a plexiglass shield. The 4000 mAh
12 volt LiPo battery is mounted to the bottom and protected by a similar plate of aluminum. If I'm flying somewhere scenic I put my
gopro camera in the mount I've put below the battery.

Flying this is hard. As I've never flown any rc aircraft before, I had to learn by
crashing dozens of times. I learned that the design of the airframe
very important (nothing should rattle or it'll get out of balance and crash), and that all nuts need to be
threadlocked or the thing will come apart in the air
(nothing is more terrifying that seeing parts fall out of your quadcopter as it's flying). Also cable management is necessary, or a prop might cut through an important
wire or cable (couple this with things falling off your quadcopter and you get some sort of hellish nightmare scenario I'd gone through far too often).

Special thanks to Alex Martin who helped tremendously to design and construct the airframe and for donating his
garage for 3 weeks.